Abstract
This work, presents a novel application of newly developed Competitive Swarm Optimizer (CSO) in solving a non-linear, non-convex and constrained Economic Load Dispatch (ELD) problem of power systems. A comparative analysis is performed between Particle Swarm Optimization (PSO) and CSO. CSO is basically inspired by the behavior of well-known PSO algorithm. Similar to PSO, CSO is also swarm based optimization technique and has both cognitive as well as social component. The difference lies in the fact that CSO neither uses local best nor global best in updating the position of their particles, which makes the algorithm memory free. A pair wise competition is performed and only loser particles are updated after getting experience from the winner one. The performance of algorithm is tested on 4 benchmark systems with 5 case studies. Case studies include both small as well as bigger system with various degree of constraints such as; Power balance, Prohibited Operating Zone (POZ), ramp limits, valve point loading etc. Moreover, general and standard statistical tests (t-test) are also performed to investigate the consistency and robust of the proposed algorithm. The performance of CSO is significantly dependent on its social factor (ϕ) and population size. In view of this, in the present work the performance of CSO with the variation in population size and (ϕ) are also studied. Parametric study is also performed for all cases to judge the sensitivity of the algorithm. The study reveals that the proper tuning of social factor (ϕ) and population size significantly reduce the search space which helps the algorithm to accelerate its convergence.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
J. Wood, B.F. Wollenberg, in Power Generation Operation and Control, 2nd edn. (Wiley, Hoboken, 2013)
N. Sinha, R. Chakrabati, P.K. Chattopadhyay, Evolutionary programming techniques for economic load dispatch. IEEE Trans. Evol. Comput. 7(1), 83–94 (2003). https://doi.org/10.1109/TEVC.2002.806788
A. Pereira-Neto, C. Unsihuay, O.R. Saavedra, Efficient evolutionary strategy optimization procedure to solve the nonconvex economic dispatch problem with generator constraints. IEE Proc. Gener. Transm. Distrib. 152(5), 653–660 (2005). https://doi.org/10.1049/ip-gtd:20045287
D. Liu, Y. Cai, Taguchi method for solving the economic dispatch problem with non smooth cost functions. IET Gener. Transm. Distrib. 1(5), 793–803 (2007). https://doi.org/10.1109/TPWRS.2005.857939
C.L. Chiang, Genetic-based algorithm for power economic load dispatch. IEE Proc. Gener. Transm. Distrib. 1(2), 261–269 (2007). https://doi.org/10.1049/iet-gtd:20060130
J.S. Al-Sumait, A.K. Al-Othmam, J.K. Sykulski, Application of pattern search method to power system valve-point economic load dispatch. Electr. Power Energy Syst. 29(10), 720–730 (2007). https://doi.org/10.1016/j.ijepes.2007.06.016
X.-S. Yang, S.S.S. Hosseini, A.H. Gandomi, Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect. Appl. Soft Comput. 12, 1180–1186 (2012). https://doi.org/10.1016/j.asoc.2011.09.017
K.K. Vshwakarma, H.M. Dubey, Simulated annealing based optimization for solving large scale economic load dispatch problems. Int. J. Eng. Res. Technol. (IJERT) 1(3), 1–8 (2012). https://doi.org/10.4314/ijest.v4i4.6
S. Ozyon, H. Temurtas, B. Durmus, G. Kuvat, Charged system algorithm for emission constrained economic power dispatch problem. Energy 46(1), 420–430 (2012). https://doi.org/10.1016/j.energy.2012.08.008
S. Özyön, C. Yaşar, H. Temurtas, Differential evolution algorithm approach to nonconvex economic power dispatch problems with valve point effect, in 6th International Advanced Technologies Symposium IATS’11 (2011), pp. 181–186
S. Özyön, C. Yasar, H. Temurtas, Particle swarm optimization algorithm for the solution of nonconvex economic dispatch problem with valve point effect, in 7th International Conference on Electrical and Electronics Engineering, ELECO’11, vol. I (2011), pp. 101–105
S. Özyön, C. Yasar, G. Özcan, H. Temurtas, An artificial bee colony algorithm (ABC) approach to nonconvex economic power dispatch problems with valve point effect, in National Conference on Electrical, Electronics and Computer (2011), pp. 294–299
D. Aydin, S. Ozyon, Solution to non-convex economic dispatch problem with valve point effects by incremental artificial bee colony with local search. Appl. Soft Comput. 13, 2456–2466 (2013). https://doi.org/10.9790/1676-11060392101
S. Pothiya, I. Ngamroo, W. Kongprawechnon, Application of multiple tabu search algorithm to solve dynamic economic dispatch considering generator constraints. Energy Convers. Manag. 49, 506–516 (2008). https://doi.org/10.1016/j.enconman.2007.08.012
A. Bhattacharya, P.K. Chattopadhyay, Biography-based optimization for different economic load dispatch problems. IEEE Trans. Power Syst. 25(2) (2010). https://doi.org/10.1109/TPWRS.2009.2034525
B. Jeddi, V. Vahidinasab, A modified harmony search method for environmental/economic load dispatch of real-world power systems. Energy Convers. Manag. 78, 661–675 (2014). https://doi.org/10.1016/j.enconman.2013.11.027
V. Hosseinnezhad, E. Babaei, Economic load dispatch using h-PSO. Electr. Power Energy Syst. 49, 160–169 (2013). https://doi.org/10.1016/j.ijepes.2013.01.002
M. Moradi-Dalvand, B. Mohammadi-Ivatloo, A. Najafi, A. Rabiee, Continuous quick group search optimizer for solving non-convex economic dispatch problems. Electr. Power Syst. Res. 93, 93–105 (2015). https://doi.org/10.1016/j.epsr.2012.07.009
B. Shaw, V. Mukerjee, S.P. Ghoshal, Solution of economic dispatch problems by seeker optimization algorithm. Expert Syst. Appl. 39, 508–519 (2012). https://doi.org/10.1016/j.eswa.2011.07.041
S. Duman, N. Yorukeren, I.H. Altas, A novel modified hybrid PSOGSA based on fuzzy logic for non-convex economic dispatch problem with valve-point effect. Elect. Power Energy Syst. 64, 121–135 (2015). https://doi.org/10.1016/j.ijepes.2014.07.031
C. Yasar, S. Özyön, A new hybrid approach for nonconvex economic dispatch problem with valve-point effect. Energy 36(10), 5838–5845 (2011). https://doi.org/10.1016/j.energy.2011.08.041
T.N. Malik, A. Asar, M.F. Wyne, S. Akhtar, A new hybrid approach for the solution of nonconvex economic dispatch problem with valve-point effects. Electr. Power Syst. Res. 80(9), 1128–1136 (2010). https://doi.org/10.1016/j.epsr.2010.03.004
V. Ravikumar Pandi, B.K. Panigrahi, R.C. Bansal, S. Das, A. Mohapatra, Economic load dispatch using hybrid swarm intelligence based harmony search algorithm. Electr Power Compon. Syst. 39(8), 751–767. https://doi.org/10.1080/15325008.2010.541411
C.-T. Su, C.-T. Lin, New approach with a hopfield modeling framework to economic dispatch. IEEE Trans. Power Syst. 15(2) (2000). https://doi.org/10.1109/59.867138
S.H. Ling, H.H.C. Iu, K.Y. Chan, H.K. Lam, B.C.W. Yeung, F.H. Leung, Hybrid particle swarm optimization with wavelet mutation and its industrial applications. IEEE Trans. Cybern. 38(3), 743–763. https://doi.org/10.1109/TSMCB.2008.921005
T.A.A. Victoire, A.E. Jeyakumar, Hybrid PSO-SQP for economic dispatch with valve-point effect. Electr. Power Syst. Res. 71(1), 51–59 (2004). https://doi.org/10.1016/j.epsr.2003.12.017
H. Ling, F.H.F. Leung, An improved genetic algorithm with average-bound crossover and wavelet mutation operation. Soft. Comput. 11(1), 7–31 (2007). https://doi.org/10.1007/s00500-006-0049-7
A.I. Selvakumar, K. Thanushkodi, A new particle swarm optimization solution to nonconvex economic dispatch problems. IEEE Trans. Power Syst. 22(1), 42–51 (2007). https://doi.org/10.1007/s00500-006-0049-7
S.-K. Wang, J.-P. Chiou, C.-W. Liu, Nonsmooth/non-convex economic dispatch by a novel hybrid differential evolution algorithm. IET Gener. Trans. Distrib. 1(5), 793–803 (2007). https://doi.org/10.1049/iet-gtd:20070183
L.D.S. Coelho, V.C. Mariani, Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect. IEEE Trans. Power Syst. 2(2), 989–996 (2006). https://doi.org/10.1109/TPWRS.2006.873410
A.I. Selvakumar, K. Thanushkodi, Anti-predatory particle swarm optimization: solution to nonconvex economic dispatch problems. Electr. Power Syst. Res. 78, 2–10 (2008). https://doi.org/10.1016/j.epsr.2006.12.001
K.T. Chaturvedi, M. Pandit, L. Srivastava, Self-organizing hierarchical particle swarm optimization for nonconvex economic dispatch. IEEE Trans. Power Syst. 23(3), 1079–1087 (2008). https://doi.org/10.1109/TPWRS.2008.926455
B.K. Panigrahi, V.R. Pandi, Bacterial foraging optimization: Nelder-Mead hybrid algorithm for economic load dispatch. IET Gener. Trans. Distrib. 2(4), 556–565 (2008). https://doi.org/10.1049/iet-gtd:20070422
J.S. Alsumait, J.K. Sykulski, A.K. Al-Othman, A hybrid GA–PS–SQP method to solve power system valve-point economic dispatch problems. Appl. Energy 87, 1773–1781 (2010). https://doi.org/10.1016/j.apenergy.2009.10.007
K. Barisal, R.C. Prusty, Large scale economic dispatch of power systems using oppositional invasive weed optimization. Appl. Soft Comput. 29, 122–137 (2015). https://doi.org/10.1016/j.asoc.2014.12.014
K. Bhattacharjee, A. Bhattacharya, S.H. Dey, Oppositional real coded chemical reaction optimization for different economic dispatch problems. Int. J. Electr. Power Energy Syst. 55, 378–391 (2014). https://doi.org/10.1016/j.ijepes.2013.09.033
A. Bhattacharya, P.K. Chattopadhyay, Hybrid differential evolution with biogeography based optimization for solution of economic load dispatch. IEEE Trans. Power Syst. 25(4) (2010). https://doi.org/10.1109/TPWRS.2010.2043270
Y. Zhang, D. Gong, Z. Ding, A bare-bones multi-objective particle swarm optimization algorithm for environmental/economic dispatch. Inf. Sci. 192, 213–227 (2012). https://doi.org/10.1016/j.ins.2011.06.004
D. Gong, Y. Zhang, C. Qi, Environmental/economic power dispatch using a hybrid multi-objective optimization algorithm. Int. J. Electr. Power Energy Syst. 32(6), 607–614 (2010). https://doi.org/10.1016/j.ijepes.2009.11.017
V. Vahidinasab, S. Jadid, Joint economic and emission dispatch in energy market: a multiobjective programming approach. Energy 35, 1497–1504 (2010). https://doi.org/10.1016/j.energy.2009.12.007
B.K. Panigrahi, P.V. Ravikumar, D. Sanjoy, D. Swagatam, Multiobjective fuzzy dominance based bacterial foraging algorithm to solve economic emission dispatch problem. Energy 35(12), 4761–4770 (2010). https://doi.org/10.1016/j.energy.2010.09.014
J. Cai, X. Ma, Q. Li, L. Li, H. Peng, A multi-objective chaotic ant swarm optimization for environmental/economic dispatch. Int. J. Electr. Power Energy Syst. 32(5), 337–344 (2010). https://doi.org/10.1016/j.ijepes.2010.01.006
M.A. Abido, Multiobjective particle swarm optimization for environmental economic dispatch problem. Elec. Power Syst. Res. 79(7), 1105–1113 (2009). https://doi.org/10.1016/j.epsr.2009.02.005
J. Hazra, A.K. Sinha, A multi-objective optimal power flow using particle swarm optimization. Eur. Trans. Electr. Power 21(1), 1028–1045 (2011). https://doi.org/10.1002/etep.494
J. Cai, X. Ma, Q. Li, L. Li, H. Peng, A multi-objective chaotic particle swarm optimization for environmental/economic dispatch. Energy Convers. Manag. 50(5), 1318–1325 (2009). https://doi.org/10.1016/j.enconman.2009.01.013
L.H. Wu, Y.N. Wang, X.F. Yuan, S.W. Zhou, Environmental/economic power dispatch problem using multi-objective differential evolution algorithm. Electr. Power Syst. Res. 80(9), 1171–1181 (2010). https://doi.org/10.1016/j.epsr.2010.03.010
M.A. Abido, Multiobjective evolutionary algorithm for electric power dispatch problem. IEEE Trans. Evol. Comput. 10(3), 315–329 (2006). https://doi.org/10.1109/TEVC.2005.857073
M.A. Abido, A novel multiobjective evolutionary algorithm for environmental economic power dispatch. Electr. Power Syst. Res. 65(1), 71–81 (2003). https://doi.org/10.1016/S0378-7796(02)00221-3
M.A. Abido, A niched pareto genetic algorithm for multiobjective environmental economic power dispatch. Int. J. Electr. Power Energy Syst. 25(2), 97–105 (2003). https://doi.org/10.1016/S0142-0615(02)00027-3
R.T.F.A. King, H.C.S. Rughooputh, K. Deb, Evolutionary multi-objective environmental/economic dispatch: stochactic vs. deterministic approaches, in Lecture Notes in Computer Science, Evolutionary Multi-Criterion Optimization, vol. 34, no. 10 (2005), pp. 677–691. https://doi.org/10.1007/978-3-540-31880-4_47
K.O. Alawode, A.M. Jubril, O.A. Komolafe, Multiobjective optimal power flow using hybrid evolutionary algorithm. Int. J. Electr. Electron. Eng. 4(7), 506–511 (2010)
S. Dhanalakshmi, S. Kannan, K. Mahadevan, S. Baskar, Application of modified NSGA-II algorithm to combined economic and emission dispatch problem. Int. J. Electr. Power Energy Syst. 33(4), 992–1002 (2011). https://doi.org/10.1016/j.ijepes.2011.01.014
M.S. Osman, M.A. Abo-Sinna, A.A. Mousa, An ε-dominance based multiobjective genetic algorithm for economic emission load dispatch optimization problem. Electr. Power Syst. Res. 79(11), 1561–1567 (2009). https://doi.org/10.1016/j.epsr.2009.06.003
M.A. Abido, Environmental/economic power dispatch using multiobjective evolutionary algorithms. IEEE Trans. Power Syst. 18(4), 1529–1537 (2003). https://doi.org/10.1109/TPWRS.2003.818693
A.A.A. El Ela, M.A. Abido, S.R. Spea, Differential evolution algorithm for emission constrained economic power dispatch problem. Electr. Power Syst. Res. 80(10), 1286–1292 (2010). https://doi.org/10.1016/j.epsr.2010.04.011
P.K. Hota, A.K. Barisal, R. Chakrabarti, Economic emission load dispatch through fuzzy based bacterial foraging algorithm. Int. J. Electr. Power Energy Syst. 32(7), 794–803 (2010). https://doi.org/10.1016/j.ijepes.2010.01.016
J. Kennedy, R. Eberhart, Particle swarm optimization, in IEEE International Conference on Neural Networks, vol. 4 (1995), pp. 1942–1948. https://doi.org/10.1109/ICNN.1995.488968
T. Mahto et al., Fractional order control and simulation of wind-biomass isolated hybrid power system using particle swarm optimization. Book chapter in Applications of Artificial Intelligence Techniques in Engineering, Advances in Intelligent Systems and Computing, vol. 698 (2018), pp. 277–287. https://doi.org/10.1007/978-981-13-1819-1_28
S. Smriti et al., Special issue on intelligent tools and techniques for signals, machines and automation. J. Intell. Fuzzy Syst. 35(5), 4895–4899 (2018). https://doi.org/10.3233/JIFS-169773
T. Mahto et al., Load frequency control of a solar-diesel based isolated hybrid power system by fractional order control using particle swarm optimization. J. Intell. Fuzzy Syst. 35(5), 5055–5061 (2018). https://doi.org/10.3233/JIFS-169789
H. Malik et al., PSO-NN-based hybrid model for long-term wind speed prediction: a study on 67 cities of India, Book chapter in Applications of Artificial Intelligence Techniques in Engineering, Advances in Intelligent Systems and Computing, vol. 697, pp. 319–327 (2018). https://doi.org/10.1007/978-981-13-1822-1_29
W.-N. Chen, J. Zhang, Y. Lin, N. Chen, Z.-H. Zhan, H.S.-H. Chung, Y. Li, Y.-H. Shi, Particle swarm optimization with an aging leader and challengers. IEEE Trans. Evol. Comput. 17(2) (2013). https://doi.org/10.1109/TEVC.2011.2173577
Z.-H. Zhan, J. Zhang, Y. Li, Y.-H. Shi, Orthogonal learning particle swarm optimization. IEEE Trans. Evol. Comput. 15(6) (2011). https://doi.org/10.1109/TEVC.2010.2052054
T. Mabu Subhani, C. Satish Babu, Particle swarm optimization with time varying acceleration coefficients for economic dispatch considering valve point loading effects, in IEEE-ICCCNT (2012), pp. 1–8. https://doi.org/10.1109/ICCCNT.2012.6396022
Y. Xu, Q. Wang, J. Hu, An improved discrete particle swarm optimization based on cooperative swarms, in IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology, vol. 2, pp. 79–82 (2008). https://doi.org/10.1109/WIIAT.2008.103
R. Cheng, Y. Jin, A competitive swarm optimizer for large scale optimization. IEEE Trans. Cybern. 45(2) (2015). https://doi.org/10.1109/TCYB.2014.2322602
G. Wu, W. Pedrycz, P.N. Suganthan, R. Mallipeddi, A variable reduction strategy for evolutionary algorithms handling equality constraints. Appl. Soft Comput. 37, pp 774–786. https://doi.org/10.1016/j.asoc.2015.09.007
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Ethics declarations
Compliance with Ethical Standards
Conflict of Interest: Abhishek Rajan declares that he has no conflict of interest. Abhay Sahu declares that he has no conflict of interest. Debashish Deka declares that he has no conflict of interest. T. Malakar declares that he has no conflict of interest.
Ethical Approval: This article does not contain any studies with human participants or animals performed by any of the authors.
Appendix
Appendix
See Table 16.
Rights and permissions
Copyright information
© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Rajan, A., Sahu, A., Deka, D., Malakar, T. (2021). A Maiden Application of Competitive Swarm Optimizer for Solution of Economic Load Dispatch with Parameter Estimation. In: Malik, H., Iqbal, A., Joshi, P., Agrawal, S., Bakhsh, F.I. (eds) Metaheuristic and Evolutionary Computation: Algorithms and Applications. Studies in Computational Intelligence, vol 916. Springer, Singapore. https://doi.org/10.1007/978-981-15-7571-6_14
Download citation
DOI: https://doi.org/10.1007/978-981-15-7571-6_14
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-7570-9
Online ISBN: 978-981-15-7571-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)